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The first technique that will be described is state equations. These equations contain three main parts, as shown below in Figure 12.19. To describe them simply -a state will be on if it is already on, or if it has been turned on by a transition from another state, but it will be turned off if there was a transition to another state. An equation is required for each state in the state diagram.

plc states -12.17

Informally,

State X = (State X + just arrived from another state) and has not left for another state

Formally,

STATEi = STATEi + ? (Tji•STATEj)•?(,•STATEi)

,Tik

j =1 k =1

where, STATEi = A variable that will reflect if state i is on

n = the number of transitions to state i

m = the number of transitions out of state i

= The logical condition of a transition from state j to i

Tji

= The logical condition of a transition out of state i to k

Tik

Figure 12.19 State Equations

The state equation method can be applied to the traffic light example in Figure

12.8. The first step in the process is to define variable names (or PLC memory locations) to keep track of which states are on or off. Next, the state diagram is examined, one state at a time. The first equation if for ST1, or state 1 -green NS.

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